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Low-frequency (DC) gain of LTI system

`k = dcgain(sys) `

`k = dcgain(sys) `

computes the DC gain `k`

of the LTI model `sys`

.

The continuous-time DC gain is the transfer function value at
the frequency *s* = 0.
For state-space models with matrices (*A*, *B*, *C*, *D*),
this value is

*K* = *D* – *CA*^{–1}*B*

The discrete-time DC gain is the transfer function value at *z* = 1. For state-space models with matrices
(*A*, *B*, *C*, *D*),
this value is

*K* = *D* + *C*(*I* – *A*)^{–1}*B*

The DC gain is infinite for systems with integrators.